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Controlling the Quality Factor of a Single Acoustic Nanoresonator by Tuning its Morphology Fabio Medeghini, Aurélien Crut, Marco Gandolfi, Francesco Rossella, Paolo Maioli, Fabrice Vallée, Francesco Banfi, and Natalia Del Fatti Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02096 • Publication Date (Web): 10 Jul 2018 Downloaded from http://pubs.acs.org on July 13, 2018
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Controlling the Quality Factor of a Single Acoustic Nanoresonator by Tuning its Morphology
Fabio Medeghini1, Aurélien Crut1*, Marco Gandolfi2,3,4, Francesco Rossella5, Paolo Maioli1, Fabrice Vallée1 , Francesco Banfi2 and Natalia Del Fatti1
1
FemtoNanoOptics group, Université de Lyon, CNRS, Université Claude Bernard Lyon 1, Institut Lumière Matière, F-69622 Villeurbanne, France 2
Interdisciplinary Laboratories for Advanced Materials Physics (I-LAMP), Università Cattolica del Sacro Cuore, Brescia I-25121, Italy 3
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Brescia I-25121, Italy
4
Laboratory of Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Heverlee, Leuven, Belgium 5
NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, I-56124 Pisa, Italy
ABSTRACT: The mechanical vibrations of individual gold nanodisks nanopatterned on a sapphire substrate are investigated using ultrafast time-resolved optical spectroscopy. The number and characteristics of the detected acoustic modes are found to vary with nanodisk geometry. In particular, their quality factors strongly depend on nanodisk aspect ratio (i.e., diameter over height ratio), reaching a maximal value of ≈70, higher than those previously measured for substrate-supported nanoobjects. The peculiarities of the detected acoustic vibrations are confirmed by finite-element simulations, and interpreted as the result of substrate-induced hybridization between the vibrational modes of a nanodisk. The present findings demonstrate novel possibilities for engineering the vibrational modes of nano-objects.
KEYWORDS: Nano-objects, vibrations, ultrafast, damping, substrate, hybridization
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The vibrational properties of nano-objects currently attract great interest, motivated by both fundamental questions and application possibilities. Their study provides information on the laws governing elasticity and energy transfer at the nanoscale.1–4 Moreover, their high sensitivity to mass deposition, resulting from the small mass of nano-objects and their high vibrational frequencies, makes them promising for mass sensing applications.5–12 Nano-object vibrations can be experimentally addressed using optics-based methods such as Raman and time-resolved spectroscopies, which enable the detection of a few vibrational modes and the measurement of their frequencies and, under certain conditions, of their decay rates.13–18 Experiments performed in the last twenty years in this field have clarified the dependence of vibrational frequencies on nano-object size, shape, crystallinity and environment.1,2,19–22 In particular, their surprisingly accurate reproduction by continuum mechanics models, even in the case of ultrasmall (∼1 nm) nanoparticles,23,24 has been repeatedly demonstrated. However, many questions still remain open regarding the nature and efficiency of the mechanisms ruling the vibrational damping of nano-objects. In contrast with vibrational frequencies which are predominantly determined by intrinsic nano-object properties (e.g., composition, morphology and crystallinity),1 decay rates are very sensitive to the properties of the nanoobject/environment interface, which determine the efficiency with which acoustic waves are emitted in the environment. Additionally, a quantitative investigation of damping based on measurements on ensembles of nanoparticles is challenging because of the spurious inhomogeneous effects (i.e., the fact that nanoparticles in an assembly vibrate at different frequencies due to the dispersion of their morphology) affecting these experiments. Up to now, investigations of vibrational damping on ensembles of nano-objects have thus been limited to two types of nano-objects that could be synthesized with particularly low morphological dispersion (silver nanospheres embedded in glass15 and gold bipyramids in solution4,25). The development of time-resolved experiments on single nano-objects a decade ago has paved the way to a more detailed investigation of vibrational damping, allowing direct measurement of the frequency f, decay rate Γ and quality factor Q=πf/Γ associated to the detected vibrational modes.26–29 In such experiments, the value of Q is limited by two distinct categories of damping processes, namely radiative and intrinsic damping. The former mechanism refers to the conversion of localized nano-object vibrations into propagative acoustic waves in its environment by elastic energy transfer through the nano-object surface. Its associated quality factor, Qenv, strongly depends on acoustic mismatch19 and mechanical contact quality7,10,30–35 at the interface between the nano-object and its local environment. The 2 ACS Paragon Plus Environment
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details of the latter mechanism, associated to a quality factor Qint, remain to be understood. Assuming the two mechanisms to be independent leads to the following expression for Q: ଵ ୕
=
ଵ ୕౬
+
ଵ ୕౪
(1)
Acoustic coupling with the environment is the dominant damping mechanism in experiments performed on substrate-deposited nano-objects synthesized by chemical methods.1,28,29,36 Q values in the 5-50 range were measured for their detected vibrational modes, with a large interparticle dispersion, attributed to variations of the quality of the nanoparticle/substrate mechanical contact. Lower quality factors have been recently reported for lithographed nano-objects,37–39 resulting from lower Qint values as compared to chemically synthesized ones. Experiments on nanowires suspended over a trench have the advantage to enable an experimental estimation of both Qenv and Qint by comparing the acoustic behaviour of the same nanowire in air (where Q≈Qint) and liquid environments (where Q is given by Eq. 1).40–42 As compared to nanoparticles, interpretation of the extracted Qint≈100 values is however complicated by the occurrence of an additional phenomenon, i.e. the propagation of acoustic waves along the nanowire away from its excited part.42 This overview highlights the still limited understanding of nano-object vibrational damping. In this paper, we demonstrate that the vibrational quality factors of substrate-supported nano-objects strongly depend on their morphology, and may be significantly enhanced for specific shape choices. To this end, systematic time-resolved studies were performed on individual gold nanodisks (NDs) nanopatterned on a sapphire substrate, chosen because of their potential technological relevance and of their shape, described by only two lengths, i.e., their diameter D and height h (with their aspect ratio defined as η=D/h) and allowing a large contact area with the substrate. Gold NDs with a diameter spanning the D=60-200 nm range and h≈20 or 40 nm thickness were nanopatterned by electron beam lithography (EBL) and lift-off techniques on the optically polished surface of a 480 µm thick (0001) α-Al2O3 single crystal (sapphire) substrate. The adopted procedures grant both a good morphology control and a clean disk/substrate interface. A large (10 µm) separation between NDs was chosen so as to allow optical investigation of a single ND and to avoid the acoustic cross-talk between the NDs occurring in phononic crystals12,43 and oligomers of close NDs.44 Several replicas of the above mentioned samples were built (in multiple deposition sessions) and measured so as to rule-out possible spot contamination and evaporation session-dependent effects. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) characterizations of the NDs were 3 ACS Paragon Plus Environment
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performed for a first selection of the best quality NDs. Complementary information on the circular character of the NDs was obtained by measuring their linear optical response using spatial modulation spectroscopy (SMS).45–48 This single-particle technique is based on the periodic displacement of a single nano-object in the focal spot of a tightly focused light beam, which induces a modulation of the transmitted light power (Fig. 1a). It enables the quantitative determination of the nano-object extinction cross-section σext as a function of the illumination wavelength λ and light polarization angle θ. SMS experiments were performed using a tunable Ti:sapphire oscillator combined with a visible optical parametric oscillator as light source, allowing ND optical characterization in the 540–1040 nm wavelength range. The light beam delivered by this source was focused down to the diffraction limit (about 0.7 λ full-width at half-maximum) on a sample by a 100X microscope objective, the direction of its linear polarization being controlled by a wire grid polarizer. Spatial modulation of the sample was performed at f=1.5 kHz frequency and lock-in detection at 2f. The dependence of σext on the incident light polarization direction θ shows two distinct behaviors among the individual NDs of the produced samples. For a fraction of them, σext is almost independent of θ, and its spectrum exhibits a quasi-Lorentzian peak associated to the ND dipolar localized surface plasmon resonance (SPR) (Fig. 1b-c).47,49,50 This behavior corresponds to the response expected for an ideal ND shape. Conversely, for many other NDs, marked variations of σext with θ occur, indicating a non-circular ND section, and leading to a ND acoustic response more complex and difficult to interpret. Such nano-objects were discarded in the present study. Fig. 1d shows the spectral position of SPR for the selected circular h=40 nm NDs, which linearly red-shifts for increasing ND aspect ratio. Such linear evolution is in agreement with the results of finiteelement simulations including the inhomogeneous ND environment (air and sapphire substrate) (Fig. 1d). The measured and modelled dependences however present a small shift, corresponding to an aspect ratio difference of 0.2-0.3. Such behaviour presumably results from the fabrication of NDs either cylindrical with a diameter slightly smaller (by about 10 nm) than that the nominal ones, or slightly conical, i.e. narrowing at their top (as reported in ref. 37). Time-resolved experiments on individual NDs (Fig. 1e) were then performed by combining the SMS microscope with a two-color pump-probe setup based on the previously described femtosecond laser source, delivering ∼150 fs pulses. The oscillator pulse train was split in two parts to generate the pump and probe beams, a different wavelength being generated for one of them using either second harmonic generation or the optical parameter oscillator. Incident pump fluences of a few hundreds of µJ.cm-2 were typically used. The relative changes of probe beam transmission, ∆T/T, were measured as a function of the time
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interval separating pump and probe pulses, controlled by a mechanical delay line. The timeresolved signal measured for a ND with D=150 nm and h=40 nm (i.e., η=3.75) using a λ=950 nm probe wavelength is shown as an example in Fig. 1f. It contains signatures of the creation of an athermal electronic distribution by pump pulse absorption and the induced relaxation mechanisms. The peak observed at short timescales reflects the ND ultrafast excitation and the internal gold thermalization on a ≈1 ps timescale (by electron-electron and electronphonon scattering mechanisms, process 1 in Fig. 1f).51 This impulsively launches ND acoustic vibrations (by a displacive excitation mechanism induced by thermal dilation), causing damped oscillations of time-resolved signals on nanosecond timescales (process 2 in Fig. 1f).1 This feature partly overlaps with a monotonic decay of the signal associated to ND cooling52 (i.e., dissipation of the thermal energy injected by the pump pulse also occurring on a nanosecond timescale, process 3 in Fig. 1f). The oscillating components of the measured time-resolved signals were isolated by subtraction of the internal thermalization and cooling contributions (Fig. 2). Each of the resulting signals was then fitted by one or two (depending on ND aspect ratio η) damped sinusoids, each associated to the contribution of a specific vibrational mode, allowing determination of its frequency, decay rate (and thus quality factor) and amplitude. The oscillating signals obtained for η>3.2 could be well fitted by a single damped sinusoid, corresponding to the detection of a single vibrational mode (the η=3.5 case is shown in Fig. 2a). Conversely, for 2.2
